When a catastrophe occurs insurance companies face a potentially excessive number of property claims. Although the term catastrophe is defined by Property Claim Services, PCS, as being a single occurrence that generates insured losses exceeding $25 million, insurance companies often use the term to describe any event producing extensive damage resulting in a large number of claims. While most catastrophes are weather-related, involving hurricanes, winter storms, and tornadoes, severe damage may also be caused by earthquakes and brush fires. When a catastrophe occurs often too many claims are made in a short period of time creating a number of serious problems related to an insurance company's surplus which is a company's net worth after subtracting liabilities from assets. The most devastating result would be insolvency. If the surplus is depleted too far, then the insurance company will be unable to fulfill its obligations to its policyholders. Because of the wide impact of insolvency, government regulation of the insurance industry is strict and each company is required to maintain a minimum surplus. A further problem for insurance companies is the rating system. Competition in the insurance industry has become fierce making published ratings more critical. The size of a company's surplus is a key factor analysts use to determine a company's rating. Therefore, a company which hopes to compete in the insurance market must take appropriate steps to ensure that its surplus is maintained. To maintain its surplus and protect against insolvency insurance companies may purchase one or more reinsurance policies.
An insurance company, also known as a primary or ceding company, buys reinsurance from a reinsurance company in much the same way that direct or primary insurance is purchased. When an insurance company purchases reinsurance it spreads a portion of the risk it has assumed to the reinsurance company. There are many different forms of reinsurance several of which may provide coverage when a catastrophe occurs. One such type that provides catastrophe protection is a quota share policy. Under this policy, a fixed proportion of all risks accepted by the primary insurer are ceded to the reinsurer. Another type of catastrophe protection is provided by excess of loss reinsurance. This form of reinsurance has expanded greatly in recent years to address the need for catastrophe protection. The excess of loss form of reinsurance includes two types, risk basis and occurrence basis. Under the risk basis type, the reinsurer pays any loss on an individual risk in excess of a predetermined amount. The other type of excess of loss, occurrence basis, is the only type of reinsurance specifically designed to provide catastrophe relief. When an insurance company purchases this type of reinsurance, the reinsurer pays when the aggregate loss from any one occurrence exceeds a predetermined retention or priority. See Generally.
(1) Reinsurance, by Carter, Merchantile & General Reinsurance Company Limited, pp. 3-12, and 59-71 (1979). PA1 (2) Reinsurance: Fundamentals and Current Issues, by Gastel, et al., Insurance Information Institute, pp. 10-21 (1983). PA1 (3) Underwriting Decisions under Uncertainty, Ayling, Gower Publishing Company, pp. 3-14 (1984). PA1 (4) Operations of Life and Health Insurance Companies, by Higgins, LOMA (Life Office Management Association, Inc.), pp. 210-216 (1986). PA1 (1) Fuzzy Logic: A Practical Approach, by McNeill, et al., AP Professional, 1994. PA1 (2) The Fuzzy Systems Handbook, by Cox, AP Professional, 1994.
Once an insurance company has purchased various types of reinsurance, its problems are not completely solved. For reinsurance to serve its purpose an insurance company must be able to collect payments due from the reinsurance company. While this may appear a simple matter, to collect the payments the insurance company must submit to the reinsurer a list of all claims relating to a given catastrophe. This list is known as a claims bordero. To create this list insurance companies first store in a computer system the information collected by insurance agents and claim adjusters for all claims made. Normally, when claims are submitted, the agent should include a catastrophe code, or CAT code, if appropriate, which indicates that the damage was caused by a particular event. The PCS assigns code numbers to catastrophes causing greater than $25 million in insured losses, and companies will often use these numbers. While this helps to standardize communications among insurance companies and reinsurers, use of these numbers is not required and an insurance company may assign its own code numbers. After storing the claims information, including CAT codes, insurance companies use complex software programs to sort through the data and compile a list of all the claims with a particular CAT code. The computer then determines, based on the types of reinsurance purchased, which claims or amounts should be submitted to the reinsurance company.
A claim is only included in the list if it has been flagged for the computer with a CAT code. Codes may be omitted for a number of reasons. Given the circumstances following a disaster, codes may be omitted by accident. Storms result in confusion and panic with large numbers of claims being processed in haste. A code might also be omitted because of a data entry error. Further, payments are often made before the true extent of the damage is realized. Even if the original claim was properly flagged, payments made at a later date may not be. Damage may not be discovered for a long time, as with water and roof damage and damage to second homes. Such claims when made may not be properly identified with a CAT code. In addition, mobile property such as motor homes, automobiles and heavy equipment may suffer catastrophe damage thousands of miles away from the insured home location. The home agent who handles the claim may not be aware that a catastrophe occurred. For each claim that is missed, the insurance company is unable to collect the payment which it is owed by the reinsurer. While the system described above is efficient at identifying claims which are labeled with CAT codes, a method is needed to identify those claims which have not been appropriately labeled.
An approach to representing knowledge has emerged in the last thirty years which has become a rapidly developing technology. Known as fuzzy logic, this tool for knowledge modeling is used to handle the uncertainty in the world around us. This uncertainty, or fuzziness, is inadequately addressed in traditional Boolean logic and original (0 or 1) set theory. Fuzzy logic systems are described, for example, in the following publications:
Any logic system consists of variables, sets and rules. Existing systems, based on original set theory, which is the basis for binary code, evaluate truth based on its existence or non-existence. Membership in a set is determined by asking whether something is a member and answering yes or no. This type of thinking, also known as crisp logic, is flawed in that truth often lies between existence and non-existence. To describe these situations which are somewhere in the middle, or fuzzy, fuzzy logic uses linguistic variables. Fuzzy sets can then be created which are associated with a linguistic variable. Each member of the set is assigned a degree of membership or degree of belonging in the set, the degree usually being represented by a percentage. Crisp logic is incorporated into fuzzy logic at the extremities. Members of a fuzzy set with a degree of membership of 0 and 100% correspond to crisp logic values 0 and 1.
Linguistic variables and fuzzy sets are then used to create fuzzy rules which are the basis of a fuzzy system. An advantage of fuzzy logic is that once translated from crisp data to linguistic variables and fuzzy sets, information may be manipulated by the well-established principles of mathematics. At the end of the process, the information is again translated and outputted as crisp data. These fuzzy systems are capable of simply describing complex, non-linear systems.
Fuzzy logic has been used in conjunction with neural networks combining the former's ability to deal with uncertainty with the latter's ability to classify and to pattern match. Modeled after the functioning of neurons in the human brain, a neural network consists of a system of nodes and weighted links. Signals to a given node are strengthened if they lead to a correct result and weakened if they lead to an incorrect result which "teaches" the network a pattern which may be used to process new data. Neural networks are not based on rules and logic structures. Fuzzy systems have been used as control systems for neural networks while neural networks have been used to produce fuzzy rules.
Insurance companies lose quite large sums of money each year because their existing computer systems are unable to identify every claim that is subject to reinsurance coverage. A system incorporating the emerging logic systems which could practically identify otherwise lost reinsurance claims from the millions of candidate claims encountered by insurance companies would be most beneficial to the industry.